sin^2 0+sin^2 1+sin^2 2....sin^2 90

$$\\sin^2 0+sin^2 1+sin^2 2....sin^2 90\\\\ =[sin^2 0+sin^2 1+...sin^244]\;\;\;+\;\;\;sin^245\;\;[+sin^246+....sin^2 90]\\\\ =(sin^2 0+sin^2 90)+....(sin^244+sin^246)+sin^245 \\\\ =(sin^2 0+cos^20)+....(sin^244+cos^244)\;\;+sin^245 \\\\ =(1)+....(1)\;\;+sin^245 \\\\ =45+sin^245\\\\ =45+(\frac{1}{\sqrt2})^2\\\\ =45\frac{1}{2}\\\\$$